Sampling theorem and reconstruction formula for the space of translates on the Heisenberg group

2019/02/05 by Arati, S., Radha, R.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1902.01531

Abstract

The paper deals with the necessary and sufficient conditions for obtaining reconstruction formulae and sampling theorems for every function belonging to the principal shift invariant subspace of L²(ℍⁿ), both in the time domain and a transform domain, where ℍⁿ denotes the Heisenberg group.

Related

• Sampling theorems for the Heisenberg groups
• Shift-invariant Spaces with Countably Many Mutually Orthogonal Generators on the Heisenberg group
• A Frequency Space for the Heisenberg Group
• Green's function for certain domains in the Heisenberg Group \mathbb H_n
• HRT Conjecture and Linear Independence of Translates on the Heisenberg Group